As a corneal surgery apparatus for ablating a cornea with a pulsed ultraviolet (UV) laser beam such as an excimer laser, there is known an apparatus which have a configuration such that an irradiation position of a laser beam is changed two-dimensionally on a cornea using a galvano mirror or other components (See Japanese Patent Application Unexamined Publication No. Hei11-226048). An apparatus of this kind has an eye tracking function which is arranged to track movement of an eye during a surgical operation, and irradiate an intended position with a laser beam. As the eye tracking function, there is known an eye tracking function which is arranged to pick up an anterior-segment image of a patient's eye with an image-pickup camera, and detects change in eye position including eye torsion by detecting a pupil edge that is a boundary of a pupil and an iris in the anterior-segment image, and an iris pattern (See published Japanese translation of PCT international publication for patent application No. 2003-511206).